WASHINGTON — Senate Majority Leader Harry Reid, D-Nev., said he will try to advance gun legislation Thursday in the Senate as some Republicans say they will attempt to block consideration.

“I’m going forward on this,” Reid told reporters at the Capitol. “The American people deserve a vote.”

While Reid said he didn’t know whether he has enough votes to prevent Republicans from using procedural tactics to block the measure, a leadership aide said Democrats are confident they will gain enough support in the coming days.

A group of Republican senators said they won’t join an effort by Minority Leader Mitch McConnell, R-Ky., and 13 other party members to prevent debate.

“It’s incomprehensible to me that we would not move forward with debate and amendments on an issue that’s so important to the American people,” said Sen. John McCain, R-Ariz.

Joining McCain in saying they wouldn’t block debate were Sens. Johnny Isakson of Georgia, Pat Toomey of Pennsylvania, Kelly Ayotte of New Hampshire and Susan Collins of Maine.

Senate Democratic leaders are trying to advance a package of gun-safety legislation including measures to crack down on gun trafficking, increase funding for school safety and require gun purchasers to undergo background checks. The legislation was proposed after 20 children and six adults were killed Dec. 14 in a shooting at an elementary school in Newtown, Conn.

Sixty votes are required to advance the measure in the Senate, where 55 votes are currently controlled by Democrats.

A few Democrats said they may join that effort. Even if Democrats can overcome the procedural hurdle, they may not have enough votes for a proposal to expand background checks to most gun purchases. Democrats are negotiating with Republicans on that measure.

President Obama is campaigning to keep momentum going for what’s left of the gun-control measures he proposed in January after the shootings in Newtown.

His call to revive a ban on military-style semiautomatic rifles and to limit ammunition-magazine capacity have encountered opposition from the National Rifle Association, the nation’s biggest gun-rights lobby, and its allies in Congress. Those proposals were excluded from the Senate bill and will be offered as amendments, which stand little chance of adoption.

Relatives of victims of the Newtown massacre flew to Washington on Monday night on Air Force One with the president to press lawmakers for action.

In a conference call with reporters Tuesday, the relatives declined requests to identify which senators they met with and what responses they received to their pleas. All they would say, said Nicole Hockley, whose son Dylan was killed at Sandy Hook, was that they were “received very warmly and openly.”

Sen. Joe Manchin, D-W.Va., and Toomey are discussing a plan that would expand the background-check requirement to cover gun sales over the Internet and private sales at gun shows, according to an aide who spoke on condition of anonymity. It would exempt private person-to-person sales, the aide said.

Earlier Tuesday, Reid said in an interview that he plans for an amendment on background checks to be first to get a vote if the bill reaches the floor.

“I’m hoping that there will be some agreement between Manchin and Toomey or Kirk and that that would be the first amendment,” said Reid, referring to Sen. Mark Kirk, R-Ill.

Complicating Democratic leaders’ efforts are objections from members of their party from pro-gun states. Democrats Max Baucus of Montana, Mark Pryor of Arkansas and Mark Begich of Alaska said they are considering whether to join the Republicans seeking to block the bill.

Vice President Joe Biden called it “embarrassing” that a small group of senators would block a vote on legislation that has broad public support.

“What has to happen to break through the consciousness of the people up on the Hill,” Biden said at a White House event with law enforcement officers. “The public is so far beyond where the Congress is.”

Baucus, facing re-election next year, said, “The vast majority of Montanans have a long adherence to the Second Amendment,” the constitutional guarantee of a right to bear arms.

Mandatory background checks for gun purchasers are supported by 91 percent of the public, including 96 percent of Democrats, 88 percent of Republicans and 88 percent of gun- owning households, according to a Quinnipiac University poll conducted March 27-April 1.

In the Newtown massacre, Adam Lanza, 20, killed 20 students and six educators. Court documents show he brought 10 30-round ammunition magazines into the school, reloaded six times and fired 154 bullets from an AR-15 semiautomatic rifle called a Bushmaster.

An estimated 6.6 million guns are sold each year without background checks because current law doesn’t require them for private gun sales, including those at gun shows, according to Mayors Against Illegal Guns. The group is led by New York Mayor Michael Bloomberg, majority owner of Bloomberg LP, the parent company of Bloomberg News.

Democrats want to require background checks for almost all gun sales. They also are seeking to mandate recordkeeping on background checks, which law enforcement officials say is needed to enforce the checks and trace weapons used in crimes.

Some Democrats say they are open to a compromise. “I want it as comprehensive as can be,” said Sen. Tim Kaine, D-Va. Even so, “if you took care of online sales and gun shows, it would be significant.”

NRA President David Keene has maintained that universal background checks could lead to “forced buybacks” or door-to- door confiscation of weapons by the government. The Fairfax, Va.-based NRA claims 4 million members.